{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [In Depth: k-Means Clustering](05.11-K-Means.ipynb) | [Contents](Index.ipynb) | [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) >\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.12-Gaussian-Mixtures.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# In Depth: Gaussian Mixture Models\n",
    "\n",
    "# 深入：高斯混合模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The *k*-means clustering model explored in the previous section is simple and relatively easy to understand, but its simplicity leads to practical challenges in its application.\n",
    "In particular, the non-probabilistic nature of *k*-means and its use of simple distance-from-cluster-center to assign cluster membership leads to poor performance for many real-world situations.\n",
    "In this section we will take a look at Gaussian mixture models (GMMs), which can be viewed as an extension of the ideas behind *k*-means, but can also be a powerful tool for estimation beyond simple clustering.\n",
    "\n",
    "前一小节讨论的k均值聚类模型是简单和相对容易理解的，但是简单的代价就是在实际应用中会遇到挑战。具体来说，k均值的非概率本质和其简单的依据与中心点距离来划分聚类的方式，决定了在很多真实世界情况中表现很不理想。本节中我们会学习高斯混合模型，它被认为是k均值算法的一种拓展，且能作为超越简单聚类的一个强大工具。\n",
    "\n",
    "> We begin with the standard imports:\n",
    "\n",
    "导入包："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivating GMM: Weaknesses of k-Means\n",
    "\n",
    "## 采用CMM：k均值的弱点\n",
    "\n",
    "> Let's take a look at some of the weaknesses of *k*-means and think about how we might improve the cluster model.\n",
    "As we saw in the previous section, given simple, well-separated data, *k*-means finds suitable clustering results.\n",
    "\n",
    "让我们先来看一下k均值算法的弱点，然后考虑如何能够改进它。正如上一节中我们看到的，给定简单的良好分离的数据，k均值能够找到正确的聚类结果。\n",
    "\n",
    "> For example, if we have simple blobs of data, the *k*-means algorithm can quickly label those clusters in a way that closely matches what we might do by eye:\n",
    "\n",
    "例如我们有一些简单的数据群落，k均值算法能够迅速的标记这些聚类，得到的结果符合我们肉眼观测的情况："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 生成数据\n",
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, y_true = make_blobs(n_samples=400, centers=4,\n",
    "                       cluster_std=0.60, random_state=0)\n",
    "X = X[:, ::-1] # flip axes for better plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 使用k均值进行聚类，并绘制结果\n",
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(4, random_state=0)\n",
    "labels = kmeans.fit(X).predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> From an intuitive standpoint, we might expect that the clustering assignment for some points is more certain than others: for example, there appears to be a very slight overlap between the two middle clusters, such that we might not have complete confidence in the cluster assigment of points between them.\n",
    "Unfortunately, the *k*-means model has no intrinsic measure of probability or uncertainty of cluster assignments (although it may be possible to use a bootstrap approach to estimate this uncertainty).\n",
    "For this, we must think about generalizing the model.\n",
    "\n",
    "直觉上来看，我们会发现图中某些数据点的聚类结果会比其他点的结果更加确定：例如图中中间两个聚类之间有很少量的重叠部分，这附近的数据点我们并不能非常确定的从属于其相应的聚类中。\n",
    "\n",
    "> One way to think about the *k*-means model is that it places a circle (or, in higher dimensions, a hyper-sphere) at the center of each cluster, with a radius defined by the most distant point in the cluster.\n",
    "This radius acts as a hard cutoff for cluster assignment within the training set: any point outside this circle is not considered a member of the cluster.\n",
    "We can visualize this cluster model with the following function:\n",
    "\n",
    "我们考虑k均值算法时，可以认为它是以中心点为圆心（球心），距离中心点最远的点的距离为半径的一个圆（或者在高维空间中，一个超球体）。这些范围被认为是训练集聚类的硬边界：任何边界外的数据点都不被认为是属于该聚类的。通过下面的函数可以将这个想法可视化出来："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist\n",
    "\n",
    "def plot_kmeans(kmeans, X, n_clusters=4, rseed=0, ax=None):\n",
    "    labels = kmeans.fit_predict(X)\n",
    "\n",
    "    # 绘制输入数据点\n",
    "    ax = ax or plt.gca()\n",
    "    ax.axis('equal')\n",
    "    ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n",
    "\n",
    "    # 绘制k均值模型\n",
    "    centers = kmeans.cluster_centers_\n",
    "    radii = [cdist(X[labels == i], [center]).max()\n",
    "             for i, center in enumerate(centers)]\n",
    "    for c, r in zip(centers, radii):\n",
    "        ax.add_patch(plt.Circle(c, r, fc='#CCCCCC', lw=3, alpha=0.5, zorder=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=4, random_state=0)\n",
    "plot_kmeans(kmeans, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> An important observation for *k*-means is that these cluster models *must be circular*: *k*-means has no built-in way of accounting for oblong or elliptical clusters.\n",
    "So, for example, if we take the same data and transform it, the cluster assignments end up becoming muddled:\n",
    "\n",
    "k均值一个重要的特点是这些聚类模型*必须是圆形*的：k均值没有內建的方式来处理长方形或者椭圆形的聚类。因此如果我们将同样的数据转换一下，聚类的结果将会变得混乱起来："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(13)\n",
    "X_stretched = np.dot(X, rng.randn(2, 2))\n",
    "\n",
    "kmeans = KMeans(n_clusters=4, random_state=0)\n",
    "plot_kmeans(kmeans, X_stretched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> By eye, we recognize that these transformed clusters are non-circular, and thus circular clusters would be a poor fit.\n",
    "Nevertheless, *k*-means is not flexible enough to account for this, and tries to force-fit the data into four circular clusters.\n",
    "This results in a mixing of cluster assignments where the resulting circles overlap: see especially the bottom-right of this plot.\n",
    "One might imagine addressing this particular situation by preprocessing the data with PCA (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)), but in practice there is no guarantee that such a global operation will circularize the individual data.\n",
    "\n",
    "肉眼观察可知转换后的聚类不是圆形的，因此圆形的聚类模型会导致不理想的拟合。然而，k均值并不具有这样的灵活性，仍然按照圆形将数据点分在四个聚类当中。这样导致的结果会是圆形的大面积重合：图中右下角的部分很清晰地展示了这一点。一种可能的解决方案是使用PCA（参见[深入：主成分分析](05.09-Principal-Component-Analysis.ipynb)）对数据进行预处理，但是实践当中并不能保证这样的全局操作能对所有数据集都能产生圆形的模型聚类。\n",
    "\n",
    "> These two disadvantages of *k*-means—its lack of flexibility in cluster shape and lack of probabilistic cluster assignment—mean that for many datasets (especially low-dimensional datasets) it may not perform as well as you might hope.\n",
    "\n",
    "k均值的这两个缺点，模型形状缺乏灵活性和无概率聚类本质，意味着对于很多数据集（特别是低维度数据集）来说，它可能不会按照预期那样工作。\n",
    "\n",
    "> You might imagine addressing these weaknesses by generalizing the *k*-means model: for example, you could measure uncertainty in cluster assignment by comparing the distances of each point to *all* cluster centers, rather than focusing on just the closest.\n",
    "You might also imagine allowing the cluster boundaries to be ellipses rather than circles, so as to account for non-circular clusters.\n",
    "It turns out these are two essential components of a different type of clustering model, Gaussian mixture models.\n",
    "\n",
    "你可能希望通过对k均值模型进行泛化来解决这些缺点：例如你可以通过对每个数据点计算其与*所有*的聚类中心点的距离来测算不确定度，而不是仅考虑最近的中心点。你也可以将聚类边界泛化成椭圆而不是圆形来适配非圆形聚类。这两个泛化技巧导致了另外一个的聚类模型，高斯混合模型。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generalizing E–M: Gaussian Mixture Models\n",
    "\n",
    "## 泛化期望最大化算法：高斯混合模型\n",
    "\n",
    "> A Gaussian mixture model (GMM) attempts to find a mixture of multi-dimensional Gaussian probability distributions that best model any input dataset.\n",
    "In the simplest case, GMMs can be used for finding clusters in the same manner as *k*-means:\n",
    "\n",
    "高斯混合模型（GMM）试图在输入数据集中找到多维高斯概率混合分布模型。在最简单情况下，GMM能够像k均值一样的对数据进行聚类：\n",
    "\n",
    "译者注：新版Scikit-Learn中，GMM已经改为GaussianMixture，下面代码相应修改。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.mixture import GaussianMixture\n",
    "gmm = GaussianMixture(n_components=4).fit(X)\n",
    "labels = gmm.predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But because GMM contains a probabilistic model under the hood, it is also possible to find probabilistic cluster assignments—in Scikit-Learn this is done using the ``predict_proba`` method.\n",
    "This returns a matrix of size ``[n_samples, n_clusters]`` which measures the probability that any point belongs to the given cluster:\n",
    "\n",
    "但是因为高斯混合模型还包含着概率模型在内，它还可以获得聚类的概率数据，使用Scikit-Learn中的`predict_proba`方法可以获得。该方法会返回一个`[n_samples, n_clusters]`的数组，里面包含每个数据点从属于每个聚类的概率值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.531 0.469 0.    0.   ]\n",
      " [0.    0.    1.    0.   ]\n",
      " [0.    0.    1.    0.   ]\n",
      " [1.    0.    0.    0.   ]\n",
      " [0.    0.    1.    0.   ]]\n"
     ]
    }
   ],
   "source": [
    "probs = gmm.predict_proba(X)\n",
    "print(probs[:5].round(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> We can visualize this uncertainty by, for example, making the size of each point proportional to the certainty of its prediction; looking at the following figure, we can see that it is precisely the points at the boundaries between clusters that reflect this uncertainty of cluster assignment:\n",
    "\n",
    "比方说我们可以将这种不确定度可视化成每个数据点的大小，越肯定的越大；就像下图所示，在两个聚类边界附近的数据点小一些，表明不确定性更高："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = 50 * probs.max(1) ** 2  # square emphasizes differences\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis', s=size);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Under the hood, a Gaussian mixture model is very similar to *k*-means: it uses an expectation–maximization approach which qualitatively does the following:\n",
    "\n",
    "1. Choose starting guesses for the location and shape\n",
    "\n",
    "2. Repeat until converged:\n",
    "\n",
    "   1. *E-step*: for each point, find weights encoding the probability of membership in each cluster\n",
    "   2. *M-step*: for each cluster, update its location, normalization, and shape based on *all* data points, making use of the weights\n",
    "   \n",
    "底层实现上，高斯混合模型与k均值很相似：它也使用期望最大化算法，其算法步骤如下：\n",
    "\n",
    "1. 选择初始位置和形状\n",
    "2. 重复一下步骤：\n",
    "    1. *E-step*：对每个数据点，找到其从属于每个聚类的概率值\n",
    "    2. *M-step*：对每个聚类，依据所有从属的数据点，计算更新它的位置，标准化值和形状\n",
    "\n",
    "> The result of this is that each cluster is associated not with a hard-edged sphere, but with a smooth Gaussian model.\n",
    "Just as in the *k*-means expectation–maximization approach, this algorithm can sometimes miss the globally optimal solution, and thus in practice multiple random initializations are used.\n",
    "\n",
    "这样算法得到的结果，每个聚类不是依据硬边界的圆形来区分，而是依据平滑的高斯模型来区分。不过也和k均值的期望最大化算法一样，上述算法有时也会得不到全局最优解，因此实践中也需要使用多个随机的初始值。\n",
    "\n",
    "> Let's create a function that will help us visualize the locations and shapes of the GMM clusters by drawing ellipses based on the GMM output:\n",
    "\n",
    "下面我们创建一个函数来帮助我们根据GMM输出结果来绘制聚类的位置和形状：\n",
    "\n",
    "译者注：新版Scikit-Learn的GaussianMixture评估器中已经不再使用covar_属性了，代码中修改为covariances_。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "def draw_ellipse(position, covariance, ax=None, **kwargs):\n",
    "    \"\"\"根据给定的位置和协方差绘制模型椭圆\"\"\"\n",
    "    ax = ax or plt.gca()\n",
    "    \n",
    "    # 将协方差转换为主坐标轴\n",
    "    if covariance.shape == (2, 2):\n",
    "        U, s, Vt = np.linalg.svd(covariance)\n",
    "        angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\n",
    "        width, height = 2 * np.sqrt(s)\n",
    "    else:\n",
    "        angle = 0\n",
    "        width, height = 2 * np.sqrt(covariance)\n",
    "    \n",
    "    # 绘制椭圆\n",
    "    for nsig in range(1, 4):\n",
    "        ax.add_patch(Ellipse(position, nsig * width, nsig * height,\n",
    "                             angle, **kwargs))\n",
    "        \n",
    "def plot_gmm(gmm, X, label=True, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    labels = gmm.fit(X).predict(X)\n",
    "    if label:\n",
    "        ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n",
    "    else:\n",
    "        ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2)\n",
    "    ax.axis('equal')\n",
    "    \n",
    "    w_factor = 0.2 / gmm.weights_.max()\n",
    "    for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):\n",
    "        draw_ellipse(pos, covar, alpha=w * w_factor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> With this in place, we can take a look at what the four-component GMM gives us for our initial data:\n",
    "\n",
    "有了这些函数，我们可以看一下我们前面的数据集在GMM下的模型展示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=4, random_state=42)\n",
    "plot_gmm(gmm, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Similarly, we can use the GMM approach to fit our stretched dataset; allowing for a full covariance the model will fit even very oblong, stretched-out clusters:\n",
    "\n",
    "类似的，我们可以使用GMM方法来拟合拉伸的数据集；设置完全协方差可令模型能拟合长条形、拉伸的聚类："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=4, covariance_type='full', random_state=42)\n",
    "plot_gmm(gmm, X_stretched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> This makes clear that GMM addresses the two main practical issues with *k*-means encountered before.\n",
    "\n",
    "这样能清楚看出GMM能解决前面说道的k均值的量大问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing the covariance type\n",
    "\n",
    "### 选择协方差的类型\n",
    "\n",
    "> If you look at the details of the preceding fits, you will see that the ``covariance_type`` option was set differently within each.\n",
    "This hyperparameter controls the degrees of freedom in the shape of each cluster; it is essential to set this carefully for any given problem.\n",
    "The default is ``covariance_type=\"diag\"``, which means that the size of the cluster along each dimension can be set independently, with the resulting ellipse constrained to align with the axes.\n",
    "A slightly simpler and faster model is ``covariance_type=\"spherical\"``, which constrains the shape of the cluster such that all dimensions are equal. The resulting clustering will have similar characteristics to that of *k*-means, though it is not entirely equivalent.\n",
    "A more complicated and computationally expensive model (especially as the number of dimensions grows) is to use ``covariance_type=\"full\"``, which allows each cluster to be modeled as an ellipse with arbitrary orientation.\n",
    "\n",
    "如果你仔细观察刚才的例子，你就会发现`covariance_type`设置是不一样的。这个超参数控制着聚类形状的自由度；对于每个不同的问题来说，小心的设置它的值是非常重要的。`covariance_type`的默认值是`'diag'`，这表示聚类形状的每个维度尺寸都可以独立的取值，结果就是聚类的形状是沿着坐标轴伸展的椭圆形。还有一个更简单和快速的模型是`covariance_type=\"spherical\"`，这样产生的结果是聚类的形状是一个圆形，在每个坐标轴上的尺寸都是相等的，因此它的效果与k均值相似，虽然两者有一定差别。还有一个更复杂和计算量大的模型（尤其是当数据的维度增加时）是`covariance_type=\"full\"`，产生的结果是每个聚类都是一个任意方向伸展的椭圆，其中每个维度的尺寸都是独立取值的。\n",
    "\n",
    "> We can see a visual representation of these three choices for a single cluster within the following figure:\n",
    "\n",
    "下面的图中我们可以看到三种不同取值的区别："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![(Covariance Type)](figures/05.12-covariance-type.png)\n",
    "[附录中生成图像的代码](06.00-Figure-Code.ipynb#Covariance-Type)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GMM as *Density Estimation*\n",
    "\n",
    "## 使用高斯混合模型作为*密度估计*\n",
    "\n",
    "> Though GMM is often categorized as a clustering algorithm, fundamentally it is an algorithm for *density estimation*.\n",
    "That is to say, the result of a GMM fit to some data is technically not a clustering model, but a generative probabilistic model describing the distribution of the data.\n",
    "\n",
    "虽然GMM经常被归为聚类算法，但它本质是一个*密度估计*算法。这就是说，GMM在一些数据上拟合的结果技术上来说不是聚合模型，而是一个生成概率模型，用来描述数据的分布。\n",
    "\n",
    "> As an example, consider some data generated from Scikit-Learn's ``make_moons`` function, which we saw in [In Depth: K-Means Clustering](05.11-K-Means.ipynb):\n",
    "\n",
    "我们用在[深入：K均值聚类](05.11-K-Means.ipynb)一节中使用Scikit-Learn的`make_moons`函数生成的数据作为例子："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "Xmoon, ymoon = make_moons(200, noise=.05, random_state=0)\n",
    "plt.scatter(Xmoon[:, 0], Xmoon[:, 1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> If we try to fit this with a two-component GMM viewed as a clustering model, the results are not particularly useful:\n",
    "\n",
    "如果我们尝试使用两个成分的GMM模型来拟合它时，产生的结果并不有意义："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm2 = GaussianMixture(n_components=2, covariance_type='full', random_state=0)\n",
    "plot_gmm(gmm2, Xmoon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> But if we instead use many more components and ignore the cluster labels, we find a fit that is much closer to the input data:\n",
    "\n",
    "但是如果我们使用更多的成分并忽略聚类产生的标签的话，我们会得到一个更接近输入数据的模型结果："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm16 = GaussianMixture(n_components=16, covariance_type='full', random_state=0)\n",
    "plot_gmm(gmm16, Xmoon, label=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Here the mixture of 16 Gaussians serves not to find separated clusters of data, but rather to model the overall *distribution* of the input data.\n",
    "This is a generative model of the distribution, meaning that the GMM gives us the recipe to generate new random data distributed similarly to our input.\n",
    "For example, here are 400 new points drawn from this 16-component GMM fit to our original data:\n",
    "\n",
    "上面的例子并不是将数据分为16个高斯混合模型聚类，而是产生了数据数据的分布模型。这就是分布生成模型，代表着GMM为我们提供了按照数据数据分布情况产生新的随机数据的方法。例如，下面是使用这个GMM模型产生400个新数据点的方法，它们将复合原始数据的分布情况：\n",
    "\n",
    "译者注：GaussianMixture的sample方法签名和返回值都发生了变化，以下代码做了相应调整。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xnew, _ = gmm16.sample(400)\n",
    "plt.scatter(Xnew[:, 0], Xnew[:, 1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> GMM is convenient as a flexible means of modeling an arbitrary multi-dimensional distribution of data.\n",
    "\n",
    "GMM可以作为产生任意多维度分布数据的生成模型的方便工具。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How many components?\n",
    "\n",
    "### 需要多少成分？\n",
    "\n",
    "> The fact that GMM is a generative model gives us a natural means of determining the optimal number of components for a given dataset.\n",
    "A generative model is inherently a probability distribution for the dataset, and so we can simply evaluate the *likelihood* of the data under the model, using cross-validation to avoid over-fitting.\n",
    "Another means of correcting for over-fitting is to adjust the model likelihoods using some analytic criterion such as the [Akaike information criterion (AIC)](https://en.wikipedia.org/wiki/Akaike_information_criterion) or the [Bayesian information criterion (BIC)](https://en.wikipedia.org/wiki/Bayesian_information_criterion).\n",
    "Scikit-Learn's ``GMM`` estimator actually includes built-in methods that compute both of these, and so it is very easy to operate on this approach.\n",
    "\n",
    "GMM是一个生成模型的事实提供给我们一个自然的方式，来获得对于给定的数据集所需的成分数量。一个生成模型实际上是数据集的概率分布，因此我们可以在模型下计算数据的*确信度*，使用交叉验证来避免过拟合。另外两个解决过拟合的方法是使用分析标准来调整模型的*确信度*，例如[赤池信息量准则(AIC)](https://zh.wikipedia.org/wiki/%E8%B5%A4%E6%B1%A0%E4%BF%A1%E6%81%AF%E9%87%8F%E5%87%86%E5%88%99)和[贝叶斯信息量准则(BIC)](https://zh.wikipedia.org/wiki/%E8%B4%9D%E5%8F%B6%E6%96%AF%E4%BF%A1%E6%81%AF%E9%87%8F%E5%87%86%E5%88%99)。Scikit-Learn的`GaussianMixture`评估器包含了內建的方法能够计算上述准则，非常方便使用。\n",
    "\n",
    "> Let's look at the AIC and BIC as a function as the number of GMM components for our moon dataset:\n",
    "\n",
    "让我们看看在上面的数据集中，AIC和BIC随着GMM成分数量变化的情况："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components = np.arange(1, 21)\n",
    "models = [GaussianMixture(n, covariance_type='full', random_state=0).fit(Xmoon)\n",
    "          for n in n_components]\n",
    "\n",
    "plt.plot(n_components, [m.bic(Xmoon) for m in models], label='BIC')\n",
    "plt.plot(n_components, [m.aic(Xmoon) for m in models], label='AIC')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('n_components');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The optimal number of clusters is the value that minimizes the AIC or BIC, depending on which approximation we wish to use. The AIC tells us that our choice of 16 components above was probably too many: around 8-12 components would have been a better choice.\n",
    "As is typical with this sort of problem, the BIC recommends a simpler model.\n",
    "\n",
    "GMM成分数量的最优选择是能最小化AIC和BIC的值，取决于我们希望应用哪种近似。上图中AIC告诉我们16个成分也许太多了：区间8-12的成分值会是更好的选择。BIC会推荐一个更简单的模型，在这类问题中是典型的情况。\n",
    "\n",
    "> Notice the important point: this choice of number of components measures how well GMM works *as a density estimator*, not how well it works *as a clustering algorithm*.\n",
    "I'd encourage you to think of GMM primarily as a density estimator, and use it for clustering only when warranted within simple datasets.\n",
    "\n",
    "注意很重要的一点：这个成分数量的选择只是衡量GMM作为*密度估计模型*的表现，不是它作为*聚类算法*的表现。作者更鼓励你将GMM主要看成是密度估计，仅在简单数据集中才保险的将它用作聚类算法。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: GMM for Generating New Data\n",
    "\n",
    "## 例子：用GMM来生成新数据\n",
    "\n",
    "> We just saw a simple example of using GMM as a generative model of data in order to create new samples from the distribution defined by the input data.\n",
    "Here we will run with this idea and generate *new handwritten digits* from the standard digits corpus that we have used before.\n",
    "\n",
    "我们刚才看到了一个用GMM作为生成模型的简单例子，模型能从输入数据的分布中产生新的样本。下面我们将使用这个思想来生成*新的手写数字*，使用的输入训练数据集是我们前面很熟悉的手写数字数据集。\n",
    "\n",
    "> To start with, let's load the digits data using Scikit-Learn's data tools:\n",
    "\n",
    "首先使用Scikit-Learn的数据工具载入手写数字数据集："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Next let's plot the first 100 of these to recall exactly what we're looking at:\n",
    "\n",
    "然后查看前面的100个样本："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig, ax = plt.subplots(10, 10, figsize=(8, 8),\n",
    "                           subplot_kw=dict(xticks=[], yticks=[]))\n",
    "    fig.subplots_adjust(hspace=0.05, wspace=0.05)\n",
    "    for i, axi in enumerate(ax.flat):\n",
    "        im = axi.imshow(data[i].reshape(8, 8), cmap='binary')\n",
    "        im.set_clim(0, 16)\n",
    "plot_digits(digits.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> We have nearly 1,800 digits in 64 dimensions, and we can build a GMM on top of these to generate more.\n",
    "GMMs can have difficulty converging in such a high dimensional space, so we will start with an invertible dimensionality reduction algorithm on the data.\n",
    "Here we will use a straightforward PCA, asking it to preserve 99% of the variance in the projected data:\n",
    "\n",
    "数据集中有接近1800个数字，每个数字都有64个维度，我们来构建一个GMM模型并且生成更多的手写数字。GMM在如此高维度空间中可能很难收敛，因此首先我们使用一个可能的降维算法来降低数据集的维度。下面我们直接使用PCA，要求它在降维后保留99%的方差："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 41)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(0.99, whiten=True)\n",
    "data = pca.fit_transform(digits.data)\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The result is 41 dimensions, a reduction of nearly 1/3 with almost no information loss.\n",
    "Given this projected data, let's use the AIC to get a gauge for the number of GMM components we should use:\n",
    "\n",
    "结果有42个维度，接近降低了1/3的维度，但是基本上没有信息的损失。在这个数据上，我们使用AIC来测算我们在GMM模型中需要使用的成分数量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components = np.arange(50, 210, 10)\n",
    "models = [GaussianMixture(n, covariance_type='full', random_state=0)\n",
    "          for n in n_components]\n",
    "aics = [model.fit(data).aic(data) for model in models]\n",
    "plt.plot(n_components, aics);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> It appears that around 110 components minimizes the AIC; we will use this model.\n",
    "Let's quickly fit this to the data and confirm that it has converged:\n",
    "\n",
    "看起来在140附近AIC具有最小值；让我们使用这个成分之来拟合数据，并查看模型收敛状态：\n",
    "\n",
    "译者注：译者运行结果为140个成分最优，因此下面代码也做了修改。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "gmm = GaussianMixture(140, covariance_type='full', random_state=0)\n",
    "gmm.fit(data)\n",
    "print(gmm.converged_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Now we can draw samples of 100 new points within this 41-dimensional projected space, using the GMM as a generative model:\n",
    "\n",
    "现在们可以使用这个GMM作为生成模型，在这个41维空间中创建100个新的数据点："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 41)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new, _ = gmm.sample(100)\n",
    "data_new.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Finally, we can use the inverse transform of the PCA object to construct the new digits:\n",
    "\n",
    "最后，我们使用PCA的逆向转换重新构建这100个手写数字："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "digits_new = pca.inverse_transform(data_new)\n",
    "plot_digits(digits_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The results for the most part look like plausible digits from the dataset!\n",
    "\n",
    "我们看到结果中大多数的数字都很符合数据集的情况。\n",
    "\n",
    "> Consider what we've done here: given a sampling of handwritten digits, we have modeled the distribution of that data in such a way that we can generate brand new samples of digits from the data: these are \"handwritten digits\" which do not individually appear in the original dataset, but rather capture the general features of the input data as modeled by the mixture model.\n",
    "Such a generative model of digits can prove very useful as a component of a Bayesian generative classifier, as we shall see in the next section.\n",
    "\n",
    "考虑一下我们这里完成的工作：给定一些手写数字的样本，我们根据数据的分布构建了模型，然后我们使用这个模型生成全新的数字样本：这些“手写数字”并不是在原始数据集中的，而是通过捕捉到输入数据的主要特征的混合模型生成的。这样的数字生成模型作为贝叶斯生成分类器的组成部分会非常有用，我们将会在下一节看到。"
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    "< [In Depth: k-Means Clustering](05.11-K-Means.ipynb) | [Contents](Index.ipynb) | [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) >\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.12-Gaussian-Mixtures.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
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